```module Data.Graph.Inductive.Query.BCC(
bcc
) where

import Data.Graph.Inductive.Graph
import Data.Graph.Inductive.Query.DFS
import Data.Graph.Inductive.Query.ArtPoint

------------------------------------------------------------------------------
-- Given a graph g, this function computes the subgraphs which are
-- g's connected components.
------------------------------------------------------------------------------
gComponents :: DynGraph gr => gr a b -> [gr a b]
gComponents g = map (\(x,y)-> mkGraph x y) (zip ln le)
where ln         = map (\x->[(u,l)|(u,l)<-vs,elem u x]) cc
le         = map (\x->[(u,v,l)|(u,v,l)<-es,elem u x]) cc
(vs,es,cc) = (labNodes g,labEdges g,components g)

embedContexts :: DynGraph gr => Context a b -> [gr a b] -> [gr a b]
embedContexts (_,v,l,s) gs = map (\(x,y)-> x & y) (zip lc gs)
where lc = map (\e->(e,v,l,e)) lc'
lc'= map (\g->[ e | e <- s, gelem (snd e) g]) gs

------------------------------------------------------------------------------
-- Given a node v and a list of graphs, this function returns the graph which
-- v belongs to, together with a list of the remaining graphs.
------------------------------------------------------------------------------
findGraph :: DynGraph gr => Node -> [gr a b] -> (Decomp gr a b, [gr a b])
findGraph _ [] = error "findGraph: empty graph list"
findGraph v (g:gs) = case match v g of
(Nothing,  g) -> let (d, gs') = findGraph v gs
in (d, g : gs')
(Just c,  g') -> ((Just c, g'), gs)

------------------------------------------------------------------------------
-- Given a graph g and its articulation points, this function disconnects g
-- for each articulation point and returns the connected components of the
-- resulting disconnected graph.
------------------------------------------------------------------------------
splitGraphs :: DynGraph gr => [gr a b] -> [Node] -> [gr a b]
splitGraphs gs []     = gs
splitGraphs [] _      = error "splitGraphs: empty graph list"
splitGraphs gs (v:vs) = splitGraphs (gs''++gs''') vs
where gs'' = embedContexts c gs'
gs' = gComponents g'
((Just c,g'), gs''') = findGraph v gs

{-|
Finds the bi-connected components of an undirected connected graph.
It first finds the articulation points of the graph. Then it disconnects the
graph on each articulation point and computes the connected components.
-}
bcc :: DynGraph gr => gr a b -> [gr a b]
bcc g = splitGraphs [g] (ap g)

```